PRICING SUPPLEMENT NO. 3                                          Rule 424(b)(3)
DATED: February 16, 2005                                     File No. 333-121744
(To Prospectus dated February 2, 2005,
and Prospectus Supplement dated February 2, 2005)

                                 $12,410,781,162
                         THE BEAR STEARNS COMPANIES INC.
                           Medium-Term Notes, Series B

Principal Amount:  $15,000,000   Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date:  2/22/2005  Fixed Rate Notes [ ]     Certificated Notes [ ]

Maturity Date:  2/16/2012        CUSIP#: 073928K28

Option to Extend Maturity:       No    [x]
                                 Yes   [ ]     Final Maturity Date:


                                                 Optional              Optional
                           Redemption            Repayment            Repayment
    Redeemable On           Price(s)              Date(s)              Price(s)
    -------------         ------------          -----------          -----------

         N/A                   N/A                  N/A                   N/A

Applicable Only to Fixed Rate Notes:
-----------------------------------

Interest Rate:

Interest Payment Dates:

Applicable Only to Floating Rate Notes:
--------------------------------------

Interest Rate Basis:                          Maximum Interest Rate:  N/A

[ ]     Commercial Paper Rate                 Minimum Interest Rate:  N/A

[ ]     Federal Funds Effective Rate

[ ]     Federal Funds Open Rate               Interest Reset Date(s):  *

[ ]     Treasury Rate                         Interest Reset Period:  Monthly

[ ]     LIBOR Reuters                         Interest Payment Date(s):  **

[x]     LIBOR Telerate

[ ]     Prime Rate

[ ]     CMT Rate

Initial Interest Rate: 2.918%                  Interest Payment Period:  Monthly

Index Maturity:  One Month

Spread (plus or minus):  +0.32%

* Commencing March 16, 2005 and on the 16th of each month thereafter prior to
Maturity.

** Commencing March 16, 2005 and on the 16th of each month thereafter, including
the maturity date.

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.